# Properties

 Label 8670.bb Number of curves $4$ Conductor $8670$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("bb1")

E.isogeny_class()

## Elliptic curves in class 8670.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8670.bb1 8670bb3 $$[1, 0, 0, -1890355, -1000519975]$$ $$30949975477232209/478125000$$ $$11540775178125000$$ $$$$ $$221184$$ $$2.2171$$
8670.bb2 8670bb2 $$[1, 0, 0, -121675, -14657743]$$ $$8253429989329/936360000$$ $$22601454108840000$$ $$[2, 2]$$ $$110592$$ $$1.8706$$
8670.bb3 8670bb1 $$[1, 0, 0, -29195, 1674225]$$ $$114013572049/15667200$$ $$378168121036800$$ $$$$ $$55296$$ $$1.5240$$ $$\Gamma_0(N)$$-optimal
8670.bb4 8670bb4 $$[1, 0, 0, 167325, -73671543]$$ $$21464092074671/109596256200$$ $$-2645387196169177800$$ $$$$ $$221184$$ $$2.2171$$

## Rank

sage: E.rank()

The elliptic curves in class 8670.bb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 8670.bb do not have complex multiplication.

## Modular form8670.2.a.bb

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 4 q^{7} + q^{8} + q^{9} + q^{10} + 4 q^{11} + q^{12} - 2 q^{13} + 4 q^{14} + q^{15} + q^{16} + q^{18} - 4 q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 